Acceleration and Escape of First Cosmic Rays Yutaka Ohira The University of Tokyo Contents � Cosmic rays, cosmic-ray heating at z <~ 20 � First supernova remnant vs. accretion shocks � Acceleration of first cosmic rays by the first SNR � Escape of first cosmic rays from the first SNR
Cosmic-ray spectrum at z = 0 1 particle/m 2 /sec Knee 1 particle/m 2 /yr When, where, how were cosmic rays first accelerated since the Big Bang? Energy flux When did the nonthermal universe start? Ohira et al., 2012 Energy
Heating of the primordial gas by CRs Sazonov & Sunyeav 2015 Leite et al. 2017 Cosmic rays can ionize and heat the primordial gas.
Observation of 21 cm line in radio Stopping length of free streaming CRs R free ~ 1Mpc ((1+z)/21) -3 (E CR /10MeV) 2 Sazonov & Sunyeav 2015 Diffusion length during the cooling time due to ionization loss (for l mfp = r g ) R diff,B ~ 30kpc ((1+z)/21) -3/2 (E CR /10MeV) 5/4 (B/10 -16 G) -1/2 Stopping length of X rays R Xray ~ 100kpc ((1+z)/21) -3 (E Xray / 0.3keV) 3.2 Mean distance between halos Information about CRs and magnetic R ~ 50kpc fields at z ~ 20 could be obtained from the observation of 21 cm line in radio.
CRs with E <~ 10 MeV heat the primordial gas Leite et al. 2017 What is the maximum energy of the first CRs? Can the first CRs escape from the source?
Diffusive Shock Acceleration(DSA) r gyro,p ~10 10 cm B -6 -1 V sh,8 -1 V sh,8 ~10 21 cm B -17 L diff ~ 10 14 cm B -6-1 E GeV ~ 10 25 cm B -17-1 E GeV Scholer CRs are scattered by Electromagnetic waves u 1 /u 2 + 2 dN/dE ∝ E -s s = = 2 Electromagnetic waves u 1 /u 2 - 1 are excited by CRs. Axford 1977, Krymsky 1977, Blandford&Ostriker 1978, Bell 1978
Acceleration time of DSA Momentum change by particle scattering, Δp After scattering, u c , p Δp = 2 p u v For a shock, shock D p per one cycle is u 1 u 2 4(u 1 - u 2 ) u 1 Δp = p = p 3v v Time of one cycle, Δt ~ residence time in the upstream region CR column density ~ n CR (D xx /u sh ) ~ n CR v Δt CR density x diffusion length CR flux x residence time t acc = p Δt/Δp ~ D xx / u sh2 ( Krymsky et al. 1979, Drury 1983)
First supernova Fi a remn mnan ants vs. ac accretion shocks Halo mass that can collapse at z=20 ~ 10 6 M sun First star are formed at z ~ 20 (Yoshida et al. 2003). M = 10 – 1000 M sun (Hirano et al. 2014) (3 s ) V sh ~ V vir ~ 10 6 cm/s M 61/3 ((1+Z)/20) 1/2 They explode at z ~ 20. Shock velocity is V sh ~ 6000km/s E SN,511/2 M ej,34-1/2 . Upstream matters are neutral. (To ionize the upstream matters, V sh > 10 7 cm/s Surrounding maters are ionized by the first stars. Dopita et al. 2011) (Kitayama et al. 2004) The shock dissipation is due to atomic collision. B ISM ~ 10 -17 G (Doi & Susa 2011). à No cosmic ray is accelerated. An unmagnetized nonrelativistic collisionless For z < 10, halos with M ~ 10 10 M sun can collapse shock is formed. and ionize the upstream matters, so that CRs could The ion Weibel instability dissipates the upstream be accelerated by the accretion shock at z < 10. ion at the shock (Kato & Takabe 2008). However, ….. Cosmic rays could be accelerated by the shock.
Io Ioniz nizatio tion n by the the fir irst t star ar Kitayama et al. 2004 HII region n ~ 1 cm -3 T ~ 1 eV f i ~ 1 ß fully ionized B < 10 -19 – 10 -17 G (Doi & Susa 2011) First supernova remnants V sh ~ 0.01c E SN,511/2 M ej,1-1/2 t Sedov ~ 1 kyr E SN,51-1/2 M ej,15/6 n ,0-1/3 R Sedov ~ 4 pc M ej,1-1/3 n ,0-1/3
Col Collision onless sh shock k of f the fi first SNR Upstream plasma: n ~ 1 cm -3 , T ~ 1 eV, f i ~ 1, B < 10 -17 G, u CMB ~ 4x10 4 eV cm -3 SNR shock: V sh ~ 0.01c E SN,511/2 M ej,1-1/2 Gyro radius r g > 1kpc >> R SNR à The initial background B is negligible. What types of collisionless shock is formed in the first SNR? 1) The Buneman is the most unstable mode (electrostatic mode). 2) Electrons are strongly heated by the Buneman instability to T e ~ m e V sh2 >> T p ~ 1eV. 3) Then, the ion-ion twostream instability becomes most unstable mode (electrostatic mode). 4) Then, ions are heated to T p ~ T e ~ m e V sh2 (Ohira & Takahara 2007,2008). 5) The ion Weibel instability becomes the most unstable mode (electromagneteic mode). Most of the kinetic energy of protons are not dissipated by the early electrostatic instabilities. Therefore, collisionless shocks driven by the first supernova remnant is nonrelativistic Weibel mediated shocks.
Weibel instability δB V d -V d e - e - δJ V d -V d e - � e - δJ V d -V d e - e - V d ⊥ k Growth rate Im[ω] = (V d /c) ω p k -1 = c / ω p Wave length
PIC simulations of Weibel mediated shocks Particle-in-cell simulations solve Maxwell equations and equation of motions for many charged particles. dN/dE ∝ E -2.4 Spectral index ~ 2.4 Spitkovsky 2008 For a relativistic Weibel mediated shock, the PIC simulation shows that particles are accelerated by DSA. For V sh ~ 0.1c, DSA is not observed in PIC because of the short simulation time. Kato & Takabe (2008)
Su Summa mmary When, where, how were first cosmic rays accelerated? First CRs could be investigated by observations of 21cm in radio. 6 Li ? Accretion shocks of the structure formation at z~20 cannot accelerate cosmic rays because the upstream gas is neutral. Supernova remnants of first stars accelerate first cosmic rays to ~ 400 MeV. CRs ( 4 MeV < E < 400 MeV ) can escape from the first SNRs and heat the primordial gas. Accretion shocks of the structure formation at z<10 can accelerate CR protons to ~300keV but they cannot escape to the far upstream because of the ionization loss. However, CR e- can escape.
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